A hypothetical reaction `:`
`A_(2)+B_(2)rarr 2AB` Follows mechanism as given below `:`
`A_(2) overset(k_(c))hArr A+A................(` fast `)" "(k_(C)-` is equilibrium constant )
`A+B_(2)overset(k_(1))rarrAB+B...............(" slow")" "(k_(1)-` rate constant )
`A+B underset(K_(2))overset(k_(2))hArrAB...............(` fast `)" "(k_(2),k_(3)-` are rate constant`)`
Give the rate law.

Options

A. `r=k_(1)sqrt(k_(c))[A_(2)]^(1//2)[B_(2)]`
B. `r=(k_(1))/(k_(c))[A_(2)]^(1//2)[B_(2)]`
C. `r=sqrt(k_(1)k_(c))[A_(2)]^(1//2)[B_(2)]`
D. `r=(k_(1))/(sqrt(k_(c)))[A_(2)]^(1//2)[B_(2)]`

Answer

A

Explanation

Rate of governed by slowest step
`A+B overset(k_(1))rarr AB+B`
`r=k_(1)[A][B_(2)]" "……(i)`
From `A_(2)overset(k_(c))hArrA+A`
`k_(c)=([A]^(2))/([A_(2)])" ".....(ii)`
`[A]=sqrt(k_(c))[A_(2)]^(1//2)`
`r=k_(1)sqrt(k_(c))[A_(2)]^(1//2)[B_(2)]" order is "=(1)/(2)+1=(3)/(2)`